Vectors — Class 12 Maharashtra HSC Mathematics revision notes
A 7-page visual revision sheet for Vectors, written for Class 12 Maharashtra HSC Mathematics. Formulas, diagrams and the traps that cost marks, laid out to be read the night before rather than the term before. Free, and it opens inside CapCompass.
What this Vectors sheet covers
- Scalars, Vectors, and the Types That Matter
- Four vectors that are easy to mix up
- Equal vectors
- Negative of a vector
- Collinear vectors
- Co-initial vectors
- Adding two vectors, two pictures of the same sum
- Laws of Vector Addition
- commutative
- associative
- additive identity and inverse
- triangle inequality
- Position Vectors and Points in Space
- Section Formula
- R divides AB internally in ratio m:n
- R divides AB externally in ratio m:n
- midpoint of AB, the case m=n
- centroid of a triangle A,B,C
- Section formula, internal and external
- Symbols
- Components, Direction Cosines and Direction Ratios
- The One Identity Every d.c. Triple Obeys
- direction cosines always satisfy
- unit vector written from its d.c.s
- d.c.s FROM d.r.s a,b,c
- Direction cosines from components
- The vector between two points
- Scalar (Dot) Product: always a number
- Dot Product, in components
- for a=a_1i+a_2j+a_3k, b=b_1i+b_2j+b_3k
- a vector dotted with itself
- angle between two vectors
- scalar projection of b on a
- vector projection of b on a
- Dot product, angle between two vectors
- Vector (Cross) Product: always a vector
- Cross Product, in components, and area
- area of the parallelogram on a and b
- area of the triangle on a and b
- Cross product and area of a triangle
- Which product do you actually need?
- Scalar Triple Product (Box Product)
- Box Product, Volumes, and the Determinant
- for a,b,c with components a_i,b_i,c_i
- volume of the parallelepiped with coterminus edges a,b,c
- volume of the tetrahedron with coterminus edges a,b,c
- coplanarity test for a,b,c
- Volume of a parallelepiped, and a coplanarity check
- Traps that cost marks
- Tricks that save time
How CapCompass uses this sheet
These notes are not a standalone PDF. CapCompass plans Mathematics chapter by chapter against your real exam dates and free hours, and when the plan reaches Vectors the sheet opens inside the study block itself — at the page covering the sub-topic that block is on, with the timer still running. Revision arrives at the moment the plan says revise, instead of having to be gone looking for.